The behavior of bounded solutions to the equation \(\Delta u-c(x)=0\) on Riemannian manifolds of special type (Q1966190)

The paper discusses the equation \(\Delta u - c(x)u = 0\), with \(c(x)\geq 0\), on complete Riemannian manifolds which are composed as the union of a compact and specific non-compact part. The examples include the Euclidean spaces, Lobachevski spaces, some rotational surfaces, etc. The main theorem discusses conditions under which bounded solutions have limits in the non--compact infinite directions and also some Liouville type results.